Extensions of the classical Cesaro operator on Hardy spaces - Curbera, Guillermo P.; Ricker, Werner J. (MATHEMATICA SCANDINAVICA, 2011)
For each 1p<∞, the classical Cesàro operator C from the Hardy space H^p to itself has the property that there exist analytic functions f otin H^p with C(f)H^p. This article deals with the identification and properties of the (Banach) space [C, H^p] consisting of all analytic functions that C maps into H^p. It is shown that [C, H^p] contains classical Banach spaces of analytic functions X, genuinely bigger that H^p, such that C has a continuous H^p-valued extension to X. An important feature is that [C, H^p] is the largest amongst all such spaces X.